纵横编织中的置换理论

在应用编织图表示纵横编织的基础上，定义了编织方格阵，然后将方格阵抽象为集合，使编织过程抽象为对集合中元素的置换。以“4步法”编织为例，应用置换理论分析了编织过程，将一个编织循环的置换结果表达成不相交的轮换的积的形式，建立了锭子运动规律与轮换表达形式的对应关系。随后，应用导出的对应关系分析了“8步法”的编织过程，计算出方格阵的初始状态，说明了置换理论对于纵横编织规律描述的普适性。

Permutation Analysis of Track and Column Braiding

The positions of braiding carrier in track and column braiding are represented by a diagrammatic braiding plan and a corresponding lattice-array is defined. A set is then formed so that the permutation analysis can be performed to represent the movement of carriers in a braiding process. The process of 4-step braiding is analyzed as an example to describe the application of the proposed method by expressing a braiding cycle as a product of disjoint cycles. As a result, a mapping relation between the disjoint cycles and the movement of carriers is deduced. Following the same analysis principles, a process of 8-step braiding and the corresponding initial state of the lattice-array is developed. A successful permutation analysis to the process manifests the general suitability of the proposed method.